Question: Given $ m \angle RPS = 8x + 7$, $ m \angle QPR = 9x + 16$, and $ m \angle QPS = 40$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Answer: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {9x + 16} + {8x + 7} = {40}$ Combine like terms: $ 17x + 23 = 40$ Subtract $23$ from both sides: $ 17x = 17$ Divide both sides by $17$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 9({1}) + 16$ Simplify: $ {m\angle QPR = 9 + 16}$ So ${m\angle QPR = 25}$.